Display for PC Gaming

Hello Guys,

Greetings to everyone in this forum! I have a few queries on which TV to purchase for my apartment. My current requirements are as follows,

Budget ~ 550$

Only and only purpose of this TV is to connect to the laptop for playing games, working from home, watching movies/TV Series, streaming videos from different sites. Would be much better if the TV Supports Bluetooth Headphones - Like this one!

My Laptop config ~ i7-2.4Ghz (3rd Gen) + 12GB RAM + GTX675M + 17.3 FHD Screen - Hence this configuration should be good enough for displaying any content more than or equal to a FHD via a HDMI Cable.

Viewing distance is around ~2.8 Meters. Please suggest me what are the scenarios/rules that needs to be taken into account while buying a TV considering aforementioned points..... Also please let me know the TV's that are good enough for a Gaming Display with my budget. Thanks in Advance! :)